Question 5

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Mark purchased packages of hamburgers for $6.75 each and B packages of buns for $1.50 each. He purchased 18 items and spent $90. Which system of equations could be used to

determine how many of each item Mark purchased?

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dfbustos dfbustos · Answer 1 · 2020-05-11T04:37:22+02:00

Answer:

[tex] B = \frac{31.5}{5.25}= 6[/tex]

[tex] H = 18-6= 12[/tex]

So then Mark purchased 12 Hamburgers and 6 packages of buns

Step-by-step explanation:

For this case we can define the following notation:

B represent the number of packages buns

H represent the number of hamburgers

And from the information given we can set up the conditions into the following equations:

[tex] 6.75 H +1.50 B =90[/tex] (1) represent the total cost

[tex] H +B =18[/tex] (2) represent the total number of items

Solving H from equation (2) we got:

[tex] H = 18 -B [/tex] (3)

And replacing equation (3) into equation (1) we got:

[tex] 6.75 (18-B) +1.5 B =90[/tex]

And dsitributing the terms we have:

[tex] 121.5 -6.75 B +1.5 B =90[/tex]

And solving for B we got:

[tex] 121.5-90 = 5.25 B[/tex]

And dividing by 5.25 we got:

[tex] B = \frac{31.5}{5.25}= 6[/tex]

And replacing the value of B into equation (3) we got:

[tex] H = 18-6= 12[/tex]

So then Mark purchased 12 Hamburgers and 6 packages of buns